Find Unit Vector Orthogonal to a & b - Help Needed

In summary, A user is new to the forum and asks for help with a calculus-related question. The question is to find a unit vector that is orthogonal to two given vectors. The user attempted to use cross products and projections, but could not get the correct answer. After receiving help and feedback from other users, they found and corrected their mistake.
  • #1
samazing18
3
0
hi! I'm new to the forums, and had a question that was more calculus-related than physics. i saw another post similar to this one, but it was incomplete and i couldn't get the answer with the information on it, any chance someone could help me out?

The question is:
"Find a unit vector with a positive first coordinate that's orthogonal to both 'a' and 'b'
a=<1,8,1>
b=<1,16,1>"

the answer i got (which is only 1/3 right) was <1/8,0,-1/8>

i've tried using cross products, and then dividing by the magnitude of the cross product to get the unit vector, but only get the j variable right, and not i and k. I've also tried projecting a onto b (and visa versa) to find parallel vectors, and then trying the cross product again, but still can't seem to get the right answer. Any ideas?
 
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  • #2


The vector you get is certainly orthogonal to both a and b, but it isn't a unit vector. This leads me to believe that you made some sort of mistake when you computed/divided by the magnitude of the cross product.
 
  • #3


morphism said:
The vector you get is certainly orthogonal to both a and b, but it isn't a unit vector. This leads me to believe that you made some sort of mistake when you computed/divided by the magnitude of the cross product.

I second this. I didn't do the work myself, but dividing the components of the vector by the magnitude of the vector is the correct method to use so you probably did make a mistake in your calculations.
 
  • #4


you're both right, and i found the error. thank's a lot
 

1. What is a unit vector?

A unit vector is a vector with a magnitude of 1 that is often used to describe the direction of a vector. It can be obtained by dividing a vector by its magnitude.

2. What does it mean for two vectors to be orthogonal?

Two vectors are orthogonal if they are perpendicular to each other, meaning they form a 90-degree angle. This can also be thought of as their dot product being equal to 0.

3. How do you find a unit vector orthogonal to two given vectors a and b?

To find a unit vector orthogonal to two given vectors a and b, you can use the cross product. The resulting vector will be perpendicular to both a and b and can then be normalized to obtain a unit vector.

4. Can there be more than one unit vector orthogonal to a and b?

Yes, there can be an infinite number of unit vectors orthogonal to a and b. This is because any vector that is perpendicular to both a and b can be normalized to obtain a unit vector.

5. In what situations would finding a unit vector orthogonal to a and b be useful?

Finding a unit vector orthogonal to a and b can be useful in many situations, such as calculating the normal vector to a plane, finding the direction of a force, or solving problems in physics and engineering involving vectors.

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